Two national civil liberties groups have sued the Labor Department, charging that a Virginia member of the Communist Workers Party was unconstitutionally barred from enrolling in a federally financed job-training program.

Dorothy Blitz, the 36-year-old Marxist now campaigning for a City Council seat in the Southside Virginia mill city of Martinsville, has been denied training because she refused to sign what her lawyers termed a loyalty oath.

"This is a throwback to lawsuits that we thought were over and done with--a throwback to the 1950s," Norman Dorsen, president of the American Civil Liberties Union, said at a news conference. "This is a throwback to McCarthyism."

The legal battle stems from a congressional measure, known as the "Blitz amendment," which prohibits persons who advocate the violent overthrow of the government from taking part in Comprehensive Employment and Training Act programs. The amendment's leading proponent was Rep. W.C. (Dan) Daniel (D-Va.), whose district includes Martinsville. The amendment took effect Dec. 15.

Last month, Virginia officials responded to the congressional move by adding a new question to its CETA application forms. It asks, "Do you now, or have you within the past five years, publicly advocated the violent overthrow of the federal government?" Blitz refused to reply, her lawyers said.

In the suit filed last week in U.S. District Court in Washington, attorneys for the ACLU and the National Emergency Civil Liberties Committee argued that the congressional measure violates Blitz's First Amendment right to free speech.

They contended the action also amounts to an unconstitutional bill of attainder, a law holding a person guilty of a crime without a trial and imposing punishment for the alleged crime. The lawyers asked for a court order requiring Blitz's CETA application to be considered "without respect to her political beliefs or association."

Blitz, who has emerged as a national cause celebre among civil liberties advocates, received CETA training in brick masonry in Martinsville for about a year. According to the lawsuit, she was granted a leave of absence last May because of pregnancy.

She applied to return to the program, which now offers a federally financed stipend of $2.55 an hour, in January but was eventually disqualified because of the congressional amendment, her lawyers said.

Meanwhile, the lawsuit contends, her family is "impoverished," subsisting in the past six months on less than $4,500 earned through occasional baby-sitting and her husband's odd jobs. Their two children are 4 1/2 years and 4 months old.

"I'm open and aboveboard about what I believe," Blitz said, describing herself as a member of the Communist Workers Party, one of several U.S.-based Marxist groups. She termed the U.S. government a "terrorist organization" and said it should be replaced with a socialist economic system.

Today, she argued, Marxists must engage in grass-roots organizing. According to her lawsuit, she believes that a "revolution may have to be accomplished by force, if necessary."

Citing several Supreme Court rulings, her lawyers contended that "advocacy of any idea--including violent revolution--is protected by the First Amendment." The government may only ban advocacy of illegal acts if it is aimed at or likely to incite imminent lawlessness, they argued.